Problem 61 - Precalculus Essentials

Question

What is the rectangular coordinate system?

Step-by-Step Solution

Answer

The rectangular coordinate system, also known as the Cartesian coordinate system, is a mathematical tool that allows for the specification of each point uniquely in a plane through two numbers, usually represented as the coordinates (x, y). For a 3D system, (x, y, z) are used. Points are located relative to an origin, which is where x and y (and z in 3D) axes intersect, and usually denoted as (0,0) or (0,0,0).

Step 1: Definition of the Rectangular Coordinate System

The rectangular coordinate system, also known as the Cartesian coordinate system, is a universally accepted system used in geometry, algebra, and calculus. It is a two-dimensional or three-dimensional system in which the position of a point is defined by its distance along perpendicular lines or axes. In a 2D Cartesian coordinate system, the horizontal line is called the x-axis and the vertical line is called the y-axis. Meanwhile, in a 3D Cartesian coordinate system, there adds another line perpendicular to the x-y plane, which is called the z-axis.

Step 2: Components of the Rectangular Coordinate System

Each axis is a number line, and every point in the rectangular coordinate system can be uniquely specified by its coordinates, which are triplets of numbers (in 3D) or pairs of numbers (in 2D). The coordinates of a point are found by drawing perpendiculars from the point to the axes (these are sometimes called its 'rectangular coordinates'). The intersection of the axes, which is the point (0,0) in 2D or (0,0,0) in 3D, is called the origin.